Technology of the 90s

16 Apr

If you never had a cassette player or a walkman, if you didn’t adjust your TV’s reception with a Yaggi antenna; if you never watched movies on the VCR or play games on Atari or SEGA; and if you never played the brick game then you were never born. And there used to be a time when 1.44 MB of a floppy disk used to be enough and people transferred data through them. A toast to these extinct technologies without which mankind would never have made the advances it has made.

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Speed Mathematics using Trachtenberg System

16 Apr

It is surprising what the human mind can achieve when it is pushed to extreme conditions. One such thing happened when a Russian Jew Jakow Trachtenberg evolved his own algorithms to do calculations speedily when he was incarcerated in the Nazi concentration camps.

Multiplication Algorithms:

2 Finger Method:

Suppose we have two numbers 120 and 131 and we want to multiply them quickly without the use of a calculator. The following figure will better illustrate what will happen:


Illustration of the 2 finger method.

Illustration of the 2 finger method.


The vertical arrow points to the product where we will get the units digit, and the sloping arrow points to the product where we will get the tens digits of the product pair. If an arrow points to a space with no digit there is no calculation for that arrow. As you solve for each digit you will move each of the arrows over the multiplicand one digit to the left until all of the arrows point to prefixed zeros.


Likewise, Trachtenberg also introduced a number of special algorithms to multiply any number by 3,4,5 and so on up till 13. For example suppose that we wanted to multiply a number by 11 then we’ll add every number to its neighbor i.e the number on it’s right side:

For example 11×37015 = 407165

3  7   0   1   5

(3+0)+1(carry from next)     (3+7)  (7+0)   (1+0)  (1+5)  (5+0)

= 4                                       0          7          1         6         5

Division Method:

The division method is pretty much the same as general multiplication method except that you have to subtract instead of adding. The division will be done in the same digit to digit way.

Addition Method:

The addition method is the usual one of writing the numbers one above the other and adding the columns together. The carry is taken over to the next digit which is something taught to us from the very beginning.


After the end of World War 2, Trachtenberg who survived the camps started to teach this method to students who did not have confidence in their abilities. It has been proven that the system can shorten calculation time by 20 percent and the results are accurate 99 percent of the time.


The practicality of knowledge

8 Apr


The canvas of imagination

6 Apr




Army and the Robots: A marriage of convenience

6 Apr
Dr. Isaac Asimov, head-and-shoulders portrait,...

Dr. Isaac Asimov, 1965 (Photo credit: Wikipedia)

Ever since Isaac Asimov put forth his famed laws governing a robot, the affair headed towards its logical outcome a marriage of convenience; in which both parties stood to gain. The army is an organization in which commands are followed to letter and spirit and this is exactly the way in which robots are programmed. While research could have been put into using the robots for peaceful purposes, man is making drones and gun mounted UGVs. If humanity understood how better off it would have been without wars, it wouldn’t have programmed humans to make them into soldiers.



It is understandable for soldiers to obey their superiors in the heat of battle without which the chain of command will collapse but in my experience, the soldiers leave no stone unturned in following the orders even in routine work. This is quite dangerous because it can make them dull as they do not make exceptions or deal with a situation in the manner it requires. For them the most important thing is the order; the higher the order comes from, the higher the need for it to be enforced.



We have been given an intellect of our own and given the ability to adapt according to changing situations. We should use those God gifted faculties instead of acting in a pre programmed way; devoid of sensing the sensitivity of the situation.